Place ground turkey, onion, bell pepper, and apple into a large skillet over medium heat. Cook until turkey is browned and crumbly, 7 to 9 minutes.
Stir ketchup, water, Dijon mustard, cider vinegar, sugar, tarragon, salt, and cloves into the skillet. Reduce heat to low and simmer for 10 minutes, adding a little more water if mixture gets a bit thick.